Example 10.6 from College Physics, 10.2 Kinematics of Rotational Motion

Calculating the Distance Traveled by a Fly on the Edge of a Microwave Oven Plate

A person decides to use a microwave oven to reheat some lunch. In the process, a fly accidentally flies into the microwave and lands on the outer edge of the rotating plate and remains there. If the plate has a radius of 0.15 m and rotates at 6.0 rpm, calculate the total distance traveled by the fly during a 2.0-min cooking period. (Ignore the start-up and slow-down times.)

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Strategy
First, find the total number of revolutions $θ$ , and then the linear distance $x$ traveled. $θ = \bar{ω} t$ can be used to find $θ$ because $\bar{ω}$ is given to be 6.0 rpm.
Solution
Entering known values into $θ = \bar{ω} t$ gives
$θ = \bar{ω} t = (6.0 rpm) (2.0 min) = 12 rev .$
10.37

As always, it is necessary to convert revolutions to radians before calculating a linear quantity like $x$ from an angular quantity like $θ$ :
$θ = (12 rev) (\frac{2 π rad}{1 rev}) = 75 .4 rad.$
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Now, using the relationship between $x$ and $θ$ , we can determine the distance traveled:

$x = rθ = (0.15 m) (75.4 rad) = 11 m .$
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Discussion
Quite a trip (if it survives)! Note that this distance is the total distance traveled by the fly. Displacement is actually zero for complete revolutions because they bring the fly back to its original position. The distinction between total distance traveled and displacement was first noted in One-Dimensional Kinematics.

0 of 3 steps open

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Strategy

Solution

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